Find original Array from given Array where each element is sum of prefix and postfix sum
Last Updated :
06 Nov, 2023
Given an array arr[] of length N, where arr is derived from an array nums[] which is lost. Array arr[] is derived as:
arr[i] = (nums[0] + nums[1] + ... + nums[i]) + (nums[i] + nums[i+1] + ... + nums[N-1]).
The task is to find nums[] array of length N.
Examples:
Input: N = 4, arr[] = {9, 10, 11, 10}
Output: {1, 2, 3, 2}
Explanation: If nums[] = {1, 2, 3, 2}, then according to above definition
arr[0] = (nums[0]) + (nums[0] + nums[1] + nums[2] + nums[3]) = 1 + 1 + 2 + 3 + 2 = 9
arr[1] = (nums[0] + nums[1]) + (nums[1] + nums[2] + nums[3]) = 1 + 2 + 2 + 3 + 2 = 10
arr[2] = (nums[0] + nums[1] + nums[2]) + (nums[2] + nums[3]) = 1 + 2 + 3 + 3 + 2 = 11
arr[3] = (nums[0] + nums[1] + nums[2] + nums[3]) + (nums[3]) = 1 + 2 + 3 + 2 + 2 = 10
Input: N = 2, arr[] = [25, 20]
Output: [10, 5]
Approach: Follow the below idea to solve the problem:
Suppose nums[] contains [a1, a2, a3, ..., aN]
Then, sum = a1 + a2 + a3 + . . . + aN.
We are given
b1 = a1 + a1 + a2 + . . . + aN = a1 + sum .....(1)
Similarly,
b2 = a1 + a2 + a2 + . . . + aN = a2 + sum .....(2)
. . . (so on) and in last
b1 = a1 + a2 + a3 + . . . + aN + aN = aN + sum .....(N)
where [b1, b2, b3 , . . ., bN] are elements of arr[] and,
total = b1 + b2 + b3 + . . . + bN
Adding all equation (1) + (2) + (3) + .... + (N) we will get
b1 + b2 + b3 + . . . + bN = (a1 + sum) + (a2 + sum) + . . . + (aN + sum)
total = (a1 + a1 + a2 + . . . + aN) + (N * sum)
total = (sum) + (N * sum)
total = (N + 1) * sum
Now find the value of sum variable after that simply:
a1 = (b1 - sum), a2 = (b2 - sum), . . ., aN = (bN - sum)
Using the above idea follow the below steps to implement the code:
- First of all, try to store the sum of elements of arr[] in a variable let's say total
- Using the formula (N + 1) * sum = total, we will get the value of variable sum which denotes the sum of elements present in the nums[] array.
- At last traverse N times to find nums[0] = arr[0] - sum, nums[1] = arr[1] - sum and so on.
- Return the array and print it.
Below is the implementation of the above approach:
C++
// C++ Algorithm for the above approach
#include <iostream>
#include <vector>
using namespace std;
// Function to find the original
// array nums[]
vector<int> findOrgArray(vector<int> arr, int N)
{
// Total variable stores the sum of
// elements of arr[]
int total = 0;
for (int val : arr)
total += val;
// Sum variable stores the sum of
// elements of nums[]
int sum = (total / (N + 1));
vector<int> v;
// Traversing to find the elements
// of nums[]
for (int i = 0; i < N; i++) {
int val = arr[i] - sum;
v.push_back(val);
}
// Returning nums[]
return v;
}
int main()
{
int N = 4;
vector<int> arr = { 9, 10, 11, 10 };
vector<int> v = findOrgArray(arr, N);
for (auto val : v)
cout << val << " ";
return 0;
}
// Java algorithm of the above approach
import java.util.*;
class GFG {
// Driver Code
public static void main(String[] args)
{
int N = 4;
int[] arr = { 9, 10, 11, 10 };
List<Integer> nums = findOrgArray(arr, N);
for (int x : nums)
System.out.print(x + " ");
}
// Function to find the original
// array nums[]
public static List<Integer> findOrgArray(int[] arr,
int N)
{
// Total variable stores the sum of
// elements of arr[]
int total = 0;
for (int val : arr)
total += val;
// Sum variable stores the sum of
// elements of nums[]
int sum = (total / (N + 1));
List<Integer> nums = new ArrayList<>();
// Traversing to find the elements
// of nums[]
for (int i = 0; i < N; i++) {
int val = arr[i] - sum;
nums.add(val);
}
// Returning nums[]
return nums;
}
}
# python3 Algorithm for the above approach
# Function to find the original
# array nums[]
def findOrgArray(arr, N) :
# Total variable stores the sum of
# elements of arr[]
total = 0
for i in arr :
total+= i
# Sum variable stores the sum of
# elements of nums[]
sum = int(total / (N + 1));
v = []
# Traversing to find the elements
# of nums[]
for i in range (N) :
val = arr[i] - sum
v.append(val)
# Returning nums[]
return v
# Driver Code
if __name__ == "__main__" :
N = 4
arr = [ 9, 10, 11, 10 ]
v = findOrgArray(arr, N)
for val in v :
print(val,end=' ')
# this code is contributed by aditya942003patil
// C# program to implement
// the above approach
using System;
using System.Collections.Generic;
public class GFG
{
// Function to find the original
// array nums[]
public static List<int> findOrgArray(int[] arr,
int N)
{
// Total variable stores the sum of
// elements of arr[]
int total = 0;
//for (int x = 0; x < arr.count; x++)
foreach (int val in arr)
total += val;
// Sum variable stores the sum of
// elements of nums[]
int sum = (total / (N + 1));
List<int> nums = new List<int>();
// Traversing to find the elements
// of nums[]
for (int i = 0; i < N; i++) {
int val = arr[i] - sum;
nums.Add(val);
}
// Returning nums[]
return nums;
}
// Driver Code
public static void Main(String []args)
{
int N = 4;
int[] arr = { 9, 10, 11, 10 };
List<int> nums = findOrgArray(arr, N);
for (int x = 0; x < nums.Count; x++)
Console.Write(nums[x] + " ");
}
}
// This code is contributed by sanjoy_62.
<script>
// Function to find the original
// array nums[]
function findOrgArray(arr, N)
{
// Total variable stores the sum of
// elements of arr[]
let total = 0;
for (let i = 0; i < N; i++)
total += arr[i];
// Sum variable stores the sum of
// elements of nums[]
let sum = (total / (N + 1));
let v= new Array(N);
// Traversing to find the elements
// of nums[]
for (let i = 0; i < N; i++) {
v[i] = arr[i] - sum;
}
// Returning nums[]
return v;
}
let N = 4;
let arr = [ 9, 10, 11, 10 ];
let v = findOrgArray(arr, N);
for (let i = 0; i < N; i++)
document.write(v[i]+ " ");
// This code is contributed by satwik4409.
</script>
Time Complexity: O(N)
Auxiliary Space: O(N), to further reduce it to O(1), store the value in the same given array arr[] rather than storing it in a new array.
Another Approach:
- Initialize a variable named "total" to 0.
- Traverse the input array "arr" using a range-based for loop.
a. For each element "val" in "arr", add "val" to the "total" variable. - Compute the sum of the original array "nums" using the formula: sum = total / (N + 1).
- Traverse the input array "arr" again using a for loop with index "i" from 0 to N-1.
a. For each element in "arr", subtract "sum" from it and store the result back into "arr[i]". This effectively undoes the modification made to "arr" and recovers the original array "nums".
Below is the implementation of the above approach:
C++
#include <iostream>
#include <vector>
using namespace std;
// Function to find the original array nums[]
void findOrgArray(vector<int>& arr, int N)
{
// Total variable stores the sum of elements of arr[]
int total = 0;
for (int val : arr)
total += val;
// Sum variable stores the sum of elements of nums[]
int sum = (total / (N + 1));
// Traversing to find the elements of nums[]
for (int i = 0; i < N; i++) {
arr[i] = arr[i] - sum;
}
}
int main()
{
int N = 4;
vector<int> arr = { 9, 10, 11, 10 };
findOrgArray(arr, N);
for (auto val : arr)
cout << val << " ";
return 0;
}
import java.util.*;
import java.io.*;
public class GFG {
// Function to find the original array nums[]
static void findOrgArray(List<Integer> arr, int N) {
// Total variable stores the sum of elements of arr[]
int total = 0;
for (int val : arr) {
total += val;
}
// Sum variable stores the sum of elements of nums[]
int sum = total / (N + 1);
// Traversing to find the elements of nums[]
for (int i = 0; i < N; i++) {
arr.set(i, arr.get(i) - sum);
}
}
// Driver Code
public static void main(String[] args) {
int N = 4;
List<Integer> arr = new ArrayList<>();
arr.add(9);
arr.add(10);
arr.add(11);
arr.add(10);
findOrgArray(arr, N);
for (int val : arr) {
System.out.print(val + " ");
}
}
}
#Function to find the original array nums[]
def find_org_array(arr, N):
total = 0 #Total variable stores the sum of elements of arr[]
for val in arr:
total += val
#Sum variable stores the sum of elements of nums[]
sum = int(total / (N + 1))
#Traversing to find the elements of nums[]
for i in range(N):
arr[i] -= sum
return arr
#Driver Code
arr=[9, 10, 11, 10]
n=4
#function call
arr=find_org_array(arr,n)
for val in arr:
print(val,end=" ")
using System;
using System.Collections.Generic;
class Program
{
// Function to find the original array nums[]
static void FindOrgArray(List<int> arr, int N)
{
// Total variable stores the sum of elements of arr[]
int total = 0;
foreach (int val in arr)
total += val;
// Sum variable stores the sum of elements of nums[]
int sum = total / (N + 1);
// Traversing to find the elements of nums[]
for (int i = 0; i < N; i++)
{
arr[i] = arr[i] - sum;
}
}
static void Main()
{
int N = 4;
List<int> arr = new List<int> { 9, 10, 11, 10 };
FindOrgArray(arr, N);
foreach (var val in arr)
Console.Write(val + " ");
}
}
// Function to find the original array nums[]
function findOrgArray(arr, N) {
// Total variable stores the sum of elements of arr[]
let total = 0;
for (let val of arr) {
total += val;
}
// Sum variable stores the sum of elements of nums[]
let sum = Math.floor(total / (N + 1));
// Traversing to find the elements of nums[]
for (let i = 0; i < N; i++) {
arr[i] = arr[i] - sum;
}
}
// Driver code
let N = 4;
let arr = [9, 10, 11, 10];
findOrgArray(arr, N);
for (let val of arr) {
console.log(val + " ");
}
Time Complexity: O(n)
Auxiliary Space: O(1)
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem